On the image-divisor method and its application

For a smooth projective 3-fold of general type, we prove that the relative canonical stability μs(3)less-than-or-equals, slant8. This is induced by our improved result of Kollár: the m-canonical map of X is birational onto its image whenever mgreater-or-equal, slanted5k+6, provided Pk(X)greater-or-equal, slanted2. The image-divisor method is intensively developed to prove our results.